With the fast development of communication techniques, over-the-air testing has developed into the main testing method for current communication systems due to its advantages including no cable connection, high measurement efficiency, and independence from environment. OTA testing has become almost the only solution for 5G system testing especially after the popularity of 5G massive multiple-input-multiple-output. In this paper, we summarize the three main methods of OTA testing including the reverberation chamber-based method, the radiation two-step method, and the multiprobe anechoic chamber- (MPAC-) based method, among which we focus on the MPAC method systematically. In the MPAC method, there are two main channel synthesis techniques that have been heavily studied, namely, prefaded signal synthesis and plane wave synthesis. We summarize the current main research based on these two techniques including probe configurations, probe selection algorithms, and probe design based on the PFS technique and the design of plane wave generators based on PWS technique. The main comparisons are made for the performance of different probe selection algorithms and the performance of different plane wave generators as well as the latest advances.